Presenter Information

David Parks, MITFollow

Description

Several aspects of the mechanical behavior of single-layer graphene are modeled from perspectives ranging from density functional theory (DFT) to finite element-based large-deformation continuum mechanics of membranes and their mechanical interactions with substrates and indentors. A novel hyperelastic constitutive formulation for the membrane response of graphene is based on joint invariants of the log strain measure and the 6th-order structure tensor comprising the C6v symmetry group of unstretched planar graphene; the resulting formulation leads to simple functional forms that accurately capture the constitutive response inferred from current and prior DFT simulations up to “large” elastic strain, along with transparent assessments of the eventual loss of strong elipticity.DFT perturbation methods provide phonon dispersion relations for the three acoustic and three optical phonons of a two-atom primitive cell in both reference and deformed configurations. Related symmetry-based coordinates are used to interpolate phonon dispersion relations over deformed invariant Brillouin zones, providing independent insights into the stability of deformed graphene with respect to both long wavelength elastic instabilities as well as soft modes having zero frequency at a nonzero wavevector. Mechanical interaction of graphene with substrates such as amorphous silica or contacting diamond nanoindentor tips occurs primarily through van der Waals interactions, which were quantified through interface traction/separation relations fit to a number of types of available experimental data, including self-tensioning of suspended membranes, blister delamination, and pull-in of pressurized membranes, with the resulting continuum finite elment simulations being in good agreement with experimental observations. Finite element simulations of the nanoindentation of suspended graphene membrane are generally in agreement with prior work by Kysar and coworkers, but the author offers new insights based on DFT and MD studies that may better explain the processes leading to final tearing failure beneath a diamond nanoindenter.

Share

COinS
 

Keynote: Multiscale mechanics of graphene

Several aspects of the mechanical behavior of single-layer graphene are modeled from perspectives ranging from density functional theory (DFT) to finite element-based large-deformation continuum mechanics of membranes and their mechanical interactions with substrates and indentors. A novel hyperelastic constitutive formulation for the membrane response of graphene is based on joint invariants of the log strain measure and the 6th-order structure tensor comprising the C6v symmetry group of unstretched planar graphene; the resulting formulation leads to simple functional forms that accurately capture the constitutive response inferred from current and prior DFT simulations up to “large” elastic strain, along with transparent assessments of the eventual loss of strong elipticity.DFT perturbation methods provide phonon dispersion relations for the three acoustic and three optical phonons of a two-atom primitive cell in both reference and deformed configurations. Related symmetry-based coordinates are used to interpolate phonon dispersion relations over deformed invariant Brillouin zones, providing independent insights into the stability of deformed graphene with respect to both long wavelength elastic instabilities as well as soft modes having zero frequency at a nonzero wavevector. Mechanical interaction of graphene with substrates such as amorphous silica or contacting diamond nanoindentor tips occurs primarily through van der Waals interactions, which were quantified through interface traction/separation relations fit to a number of types of available experimental data, including self-tensioning of suspended membranes, blister delamination, and pull-in of pressurized membranes, with the resulting continuum finite elment simulations being in good agreement with experimental observations. Finite element simulations of the nanoindentation of suspended graphene membrane are generally in agreement with prior work by Kysar and coworkers, but the author offers new insights based on DFT and MD studies that may better explain the processes leading to final tearing failure beneath a diamond nanoindenter.